We study the manipulation of slow light with an orbital angular momentum propagating in a cloud of cold atoms. Atoms are affected by four copropagating control laser beams in a double tripod configuration of the atomic energy levels involved, allowing to minimize the losses at the vortex core of the control beams. In such a situation the atomic medium is transparent for a pair of copropagating probe fields, leading to the creation of two-component (spinor) slow light. We study the interaction between the probe fields when two control beams carry optical vortices of opposite helicity. As a result, a transfer of the optical vortex takes place from the control to the probe fields without switching off and on the control beams. This feature is missing in a single tripod scheme where the optical vortex can be transferred from the control to the probe field only during either the storage or retrieval of light.
Many methods now exist to prepare free electrons into orbital angular momentum states, and the predicted applications of these electron states as probes of materials and scattering processes are numerous. The development of electron orbital angular momentum measurement techniques has lagged behind. We show that coupling between electron orbital angular momentum and a spatially varying magnetic field produces an angular momentum-dependent focusing effect. We propose a design for an orbital angular momentum measurement device built on this principle. As the method of measurement is non-interfero…
Intense laser ionization expands Einstein's photoelectric effect rules giving a wealth of phenomena widely studied over the last decades. In all cases, so far, photons were assumed to carry one unit of angular momentum. However it is now clear that photons can possess extra angular momentum, the orbital angular momentum (OAM), related to their spatial profile. We show a complete description of photoionization by OAM photons, including new selection rules involving more than one unit of angular momentum. We explore theoretically the interaction of a single electron atom located at the center of…
It is shown that the photon picture of the electromagnetic field enables one to determine unambiguously the splitting of the total angular momentum of the electromagnetic field into the orbital part and the spin part.
We present a quantum mechanical analysis of the orbital angular momentum of a class of recently discovered elliptically-symmetric stable light fields --- the so-called Ince-Gauss modes. We study, in a fully quantum formalism, how the orbital angular momentum of these beams varies with their ellipticity and discover several compelling features, including: non-monotonic behavior, stable beams with real continuous (non-integer) orbital angular momenta, and orthogonal modes with the same orbital angular momenta. We explore, and explain in detail, the reasons for this behavior. These features may h…
We propose to use an acoustic surface wave as a memory for a photon carrying orbital angular momentum. We clarify the physical mechanism that enables the transfer of information, derive the angular momentum selection rule that must be obeyed in the process, and show how to optimize the optoacoustic coupling. We theoretically demonstrate that high fidelities can be achieved, using realistic parameters, for the transfer of a coherent optical Laguerre-Gaussian state, associated with large angular momentum, to a mechanical shear mode. Our results add a significant possibility to the ongoing effort…
We consider the excitation of Rydberg states through photons carrying an intrinsic orbital angular momentum degree of freedom. Laguerre-Gauss modes, with a helical wave-front structure, correspond to such a set of laser beams, which carry some units of orbital angular momentum in their propagation direction. We demonstrate that, in a proper geometrical setting, this orbital angular momentum can be transferred to the internal degrees of freedom of the atoms, thus violating the standard dipolar selection rules. Higher orbital angular momentum states become accessible through a single photon exci…
We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum (OAM) in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.
The effect of the transversality condition on the quantization of the photon orbital angular momentum is studied. The quantum gauge that is deduced from the transversality condition is shown to be a Berry gauge. It determines a helicity-dependent reference point relative to which the position is canonically conjugate to the momentum. As a result, the photon orbital angular momentum about the origin of the laboratory reference system split into two parts. One is the orbital angular momentum of the photon about the reference point, which is canonical. The other is the orbital angular momentum of…
We present a novel method for efficient sorting of photons prepared in states of orbital angular momentum (OAM) and angular position (ANG). A log-polar optical transform is used in combination with a holographic beam-splitting method to achieve better mode discrimination and reduced cross-talk than reported previously. Simulating this method for 7 modes, we have calculated an improved mutual information of 2.43 bits/photon and 2.29 bits/photon for OAM and ANG modes respectively. In addition, we present preliminary results from an experimental implementation of this technique. This method is ex…
This paper is devoted to study the propagation of light beams carrying orbital angular momentum in optically anisotropic media. We first review some properties of homogeneous anisotropic media, and describe how the paraxial formalism is modified in order to proceed with a new approach dealing with a general setting of paraxial propagation along uniaxial inhomogeneous media. This approach is suitable for describing the space-variant-optical-axis phase plates.
We present an optomechanical device designed to allow optical transduction of orbital angular momentum of light. An optically induced twist imparted on the device by light is detected using an integrated cavity optomechanical system based on a nanobeam slot-mode photonic crystal cavity. This device could allow measurement of the orbital angular momentum of light when photons are absorbed by the mechanical element, or detection of the presence of photons when they are scattered into new orbital angular momentum states by a sub-wavelength grating patterned on the device. Such a system allows det…
In this article we investigate the orbital angular momentum spectrum of photons produced in parametric down conversion process. We study how the transverse profile of the pump mode affects the spectrum as compared to a gaussian pump beam. We show that using perfect optical vortex mode as pump the spectrum can be highly narrowed down. We further study the entanglement between the two down converted photons in the orbital angular momentum basis. We observe that photons entangled in Laguerre-Gaussian modes exhibit greater higher dimensional entanglement.
Following the very recent experimental realisation of electron vortices, we consider their interaction with matter, in particular the transfer of orbital angular momentum in the context of electron energy loss spectroscopy, and the recently observed dichroism in thin film magnetised iron samples. We show here that orbital angular momentum exchange does indeed occur between electron vortices and the internal electronic-type motion, as well as center of mass motion of atoms in the electric dipole approximation. This contrasts with the case of optical vortices where such transfer only occurs in t…
Magnetostatic modes supported by a ferromagnetic sphere have been known as the Walker modes, each of which possesses an orbital angular momentum as well as a spin angular momentum along a static magnetic field. The Walker modes with non-zero orbital angular momenta exhibit topologically non-trivial spin textures, which we call \textit{magnetic quasi-vortices}. Photons in optical whispering gallery modes supported by a dielectric sphere possess orbital and spin angular momenta forming \textit{optical vortices}. Within a ferromagnetic, as well as dielectric, sphere, two forms of vortices interac…
Optical modes with different orbital angular momentums (OAMs) per photon may be sorted by Mach-Zehnder interferometers incorporated with beam rotators, without resorting to OAM mode converters.
We review Heisenberg's uncertainty principle for the orbital angular momentum (OAM) of light. By taking into account the largest and smallest scales present in nature, such as the the Hubble radius and the Planck length, we have found that there exist upper and lower physical limits to the determination of the OAM of a photon.
We demonstrate experimentally an optical process in which the spin angular momentum carried by a circularly polarized light beam is converted into orbital angular momentum, leading to the generation of helical modes with a wavefront helicity controlled by the input polarization. This phenomenon requires the interaction of light with matter that is both optically inhomogeneous and anisotropic. The underlying physics is also associated with the so-called Pancharatnam-Berry geometrical phases involved in any inhomogeneous transformation of the optical polarization.
We demonstrate experimentally how orbital-angular-momentum entanglement of two photons evolves under influence of atmospheric turbulence. We find that the quantum channel capacity is surprisingly robust: Its typical horizontal decay distance is of the order of 2 kilometers, demonstrating the potential of photonic orbital angular momentum for free-space quantum communication in a metropolitan environment.
We report on an orbital-angular-momentum-enhanced scheme for angular displacement estimation based on two-mode squeezed vacuum and parity detection. The sub-Heisenberg-limited sensitivity for angular displacement estimation is obtained in an ideal situation. Several realistic factors are also considered, including photon loss, dark counts, response-time delay, and thermal photon noise. Our results indicate that the effects of the realistic factors on the sensitivity can be offset by raising orbital angular momentum quantum number $\ell$. This reflects that the robustness and the practicability…
The quantum theory of rotation angles (S. M. Barnett and D. T. Pegg, Phys. Rev. A, 41, 3427-3425 (1990)) is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the orientation of a phase discontinuity associated with fractional values of the orbital angular momentum. We apply our formalism to the propagation of light modes with fractional orbital angular momentum in the paraxial and non-paraxial regime.
We introduce a matter wave interference scheme based on the quantization of orbital angular momentum in a ring trap. It operates without beam splitters, is sensitive to geometric phases induced by external gauge fields, and allows measuring interatomic scattering lengths. We argue that orbital angular momentum interferometry offers a versatile platform for quantum coherent experiments with cold atoms and Bose-Einstein condensates using state-of-the-art technology.
Through scanned coincidence counting, we probe the quantum image produced by parametric down conversion with a pump beam carrying orbital angular momentum. Nonlocal spatial correlations are manifested through splitting of the coincidence spot into two.
We report on an experiment demonstrating the conservation of orbital angular momentum in stimulated down-conversion. The orbital angular momentum is not transferred to the individual beams of the spontaneous down-conversion, but it is conserved when twin photons are taken individually. We observe the conservation law for an individual beam of the down-conversion through cavity-free stimulated emission.
We study the two-photon detection amplitude of the down-converted beams in spontaneous parametric down-conversion when the physical variable of orbital angular momentum is involved, taking into account both conservation and non-conservation of angular momentum. Agreeing with experimental observations, our theoretical calculation shows that spatial structure of the two-photon detection amplitude of the down-converted beams carries important information about conservation or non-conservation of orbital angular momentum in spontaneous parametric down-conversion.
Coincidence-structures in the transverse plane of Type-II spontaneous parametric down-conversion carrying orbital angular momentum are obtained. Azimuthal symmetry breaking around the pump beam direction reveals itself on these quantum images. Analytical expressions for the amplitude probability of the down conversion process are shown including the nonlinear polarizability components.
A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.
In this paper, we propose a protocol for angular displacement estimation based upon orbital angular momentum coherent state and a SU(1,1)-SU(2) hybrid interferometer. This interferometer consists of an optical parametric amplifier, a beam splitter and reflection mirrors, hereon we use a quantum detection strategy $\---$ balanced homodyne detection. The results indicate that super-resolution and super-sensitivity can be realized with ideal condition. Additionally, we study the impact of photon loss on the resolution and the sensitivity, and the robustness of our protocol is also discussed. Fina…
A polarized photon with well-defined orbital angular momentum that emerges from a Mach-Zehnder interferometer (MZI) is shown to circumvent wave-particle duality. Its polarization-resolved detection probability forms a non-sinusoidal interferometric pattern. For certain phase differences between the MZI arms, this pattern yields both reliable which-path information and high phase-sensitivity.
In the non-linear optical process of type-II spontaneous parametric down-conversion, we present on an experiment showing that the two-photon detection amplitude of the down-converted beams does not generally reproduce the transverse profile of the pump beam that carries non-zero orbital angular momentum. We explain this observation by that orbital angular momentum is not conserved in the type-II non-linear process due to the broken rotational symmetry of the Hamiltonian.
Light carrying orbital angular momentum constitutes an important resource for both classical and quantum information technologies. Its inherently unbounded nature can be exploited to generate high-dimensional quantum states or for channel multiplexing in classical and quantum communication in order to significantly boost the data capacity and the secret key rate, respectively. While the big potentials of light owning orbital angular momentum have been widely ascertained, its technological deployment is still limited by the difficulties deriving from the fabrication of integrated and scalable p…
The paper studies the Raman quantum memory protocol as applied to quantum light with orbital angular momentum. The memory protocol is implemented on an ensemble of three-level cold atoms with the $Λ$- configuration of energy levels. The possibility of storing quantum statistics of light with an orbital momentum is analysed in the case when the driving field could be treated as a plane wave. The efficiency analysis shows that examined storage/retrieval processes do not cause the efficiency decreasing compared with the spatial multimode memory protocol considered in [Golubeva et al. 2012]]. We a…
Starting from the standard Hamiltonian describing the optical non-linear process of spontaneous parametric down-conversion, we theoretically show that the generated entangled photon-pairs carry non-negligible orbital angular momentum in the degrees of freedom of relative movement in the type-II cases due to spatial symmetry breaking. We also show that the orbital angular momentum carried by photon-pairs in these degrees of freedom escapes detection in the traditional measurement scheme, which demands development of new techniques for further experimental investigations.
We set forth a method to analyze the orbital angular momentum of a light field. Instead of using the canonical formalism for the conjugate pair angle-angular momentum, we model this latter variable by the superposition of two independent harmonic oscillators along two orthogonal axes. By describing each oscillator by a standard Wigner function, we derive, via a consistent change of variables, a comprehensive picture of the orbital angular momentum. We compare with previous approaches and show how this method works in some relevant examples.
The Shannon dimensionality of orbital angular momentum (OAM) entanglement produced in spontaneous parametric down-conversion can be probed by using multi-sector phase analysers. We demonstrate a spatial light modulator-based implementation of these analysers, and use it to measure a Schmidt number of about 50.
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially non-degenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of OAM modes is mapped on an orbital Poincare sphere, and the modes position on the sphere is spanned by the three orbital parameters. Using the non-degenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincare sphere…
Deutsch's algorithm is the simplest quantum algorithm which shows the acceleration of quantum computer. In this paper, we theoretically advance a scheme to implement quantum Deutsch's algorithm in spin-orbital angular momentum space. Our scheme exploits a newly developed optical device called "q-plate", which can couple and manipulate the spin-orbital angular momentum simultaneously. This experimental setup is of high stability and efficiency theoretically for there is no interferometer in it.
Quantum protocols will be more efficient with high-dimensional entangled states. Photons carrying orbital angular momenta can be used to create a high-dimensional entangled state. In this paper we experimentally demonstrate the entanglement of the orbital angular momentum between the Stokes and anti-Stokes photons generated in a hot atomic ensemble using spontaneous four-wave-mixing. This experiment also suggests the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.
We show that the transfer of the plane wave spectrum of the pump beam to the fourth-order transverse spatial correlation function of the two-photon field generated by spontaneous parametric down-conversion leads to the conservation and entanglement of orbital angular momentum of light. By means of a simple experimental setup based on fourth-order (or two-photon) interferometry, we show that our theoretical model provides a good description for down-converted fields carrying orbital angular momentum.
This paper analyzes the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre--Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.
We provide an analytical expression for the entanglement decay of initially maximally entangled orbital angular momentum bi-photon states, when scattered off an obstruction. We show that the decay is controlled by the diffraction-induced mutual overlap between the diffracted field modes, and quantify its dependence on the size and position of the obstruction.
Photons can carry spin angular momentum (SAM) and orbital angular momentum (OAM), which can be used to realize a qubit system and a high-dimension system respectively. This spin-orbital system is very suitable for implementing one-dimensional discrete-time quantum random walks. We propose a simple scheme of quantum walks on the spin-orbital angular momentum space of photons, where photons walk on the infinity OAM space controlled by their SAM. By employing the recent invention of an optical device, the so-called 'q-plate', our scheme is more simple and efficient than others because there is no…
We present an implementation scheme for a quantum walk in the orbital angular momentum space of a laser beam. The scheme makes use of a ring interferometer, containing a quarter-wave plate and a q plate. This setup enables one to perform an arbitrary number of quantum walk steps. In addition, the classical nature of the implementation scheme makes it possible to observe the quantum walk evolution in real time. We use nonquantum entanglement of the laser beam's polarization with its orbital angular momentum to implement the quantum walk.
We propose a new quantum network scheme using orbital angular momentum states of photons to route the network and spin angular momentum states to encode the information. A four-user experimental scheme based on this efficient quantum network is analyzed in detail, which is particularly appealing for the free space quantum key distribution. Users can freely exchange quantum keys with each other.
We analytically derive a decoherence model for orbital angular momentum states of a photon in a multimode optical fiber and show that rate of decoherence scales exponentially with $l^2$, where $l$ is the azimuthal mode order.~We also show numerically that for large values of $l$ the orbital angular momentum photon state completely dephases.~However for lower values of $l$ the decoherence can be minimized by using dynamical decoupling to allow for qudit high-bandwidth quantum communication and similar applications. \end{abstract}
We use astigmatic transformations to characterize two-dimensional superpositions of Orbital Angular Momentum (OAM) states in laser beams. We propose two methods for doing this, both relying only on astigmatic transformations, viewed as rotations on the Poincaré sphere, followed by imaging. These methods can be used as a tomographic tool for communication protocols based on optical vortices.
We investigate two-photon entangled states using two important degrees of freedom of the electromagnetic field, namely orbital angular momentum (OAM) and spin angular momentum. For photons propagating in the same direction we apply the idea of $\textit{entanglement duality}$ and develop schemes to do $\textit{entanglement sorting}$ based either on OAM or polarization. In each case the entanglement is tested using appropriate witnesses. We finally present generalizations of these ideas to three- and four-photon entangled states.
We examine the implementation of an arbitrary U(4) gate consisting of CNOT gates and single qubit unitary gates for the Hilbert space of photon spin polarization and two states of photon orbital angular momentum. Our scheme improves over a recently proposed one that uses q-plates because the fidelity is limited only by losses thus in principle it could be used to achieve a perfect transformation.
Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. We explore the ability of adaptive optics to compensate for this disturbance by measuring and correcting cumulative phase shifts in the wavefront. These shifts can be represented as a sum of Zernike functions; we analyze the residual errors after correcting up to a certain number of Zernike modes when an orbital angular momentum state is transmitted through a turbulent atmosphere whose density fluctuations have a Kolmogorov s…
The orbital angular momentum of photons, being defined in an infinitely dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum of single photons and vice versa. All our schemes exploit a newly developed op…
We study the entanglement evolution of photonic orbital angular momentum qubit states with opposite azimuthal indices $l_0$, in a weakly turbulent atmosphere. Using asymptotic methods, we deduce analytical expressions for the amplitude of turbulence-induced crosstalk between the modes $l_0$ and $-l_0$. Furthermore, we analytically establish distinct, universal entanglement decay laws for Kolmogorov's turbulence model and for two approximations thereof.
Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. Understanding the noise processes that affect photons is essential if we desire to protect them. In this paper we use the infinitesimal propagation equation of Roux to derive a discrete Lindblad equation, and numerically study the form of the most relevant Lindblad operators. We find that the dominant Lindblad operators are those that shift the angular momentum by one unit. We explore possible schemes to protect quantum infor…
We analyze the effect of Proca mass and orbital angular momentum of photons imposed by a structured plasma in Kerr-Newman and Reissner-Nordstrom-de Sitter spacetimes. The presence of characteristic lengths in a turbulent plasma converts the virtual Proca photon mass on orbital angular momentum, with the result of decreasing the virtual photon mass. The combination of this plasma effect and that of the gravitational field leads to a new astrophysical phenomenon that imprints a specific distribution of orbital angular momentum into different frequencies of the light emitted from the neighborhood…
This paper claims that local space-time curvature can non-trivially contribute to the properties of orbital angular momentum in quantum mechanics. Of key importance is the demonstration that an extended orbital angular momentum operator due to gravitation can identify the existence of orbital states with half-integer projection quantum numbers "m" along the axis of quantization, while still preserving integer-valued orbital quantum numbers "l" for a simply connected topology. The consequences of this possibility are explored in depth, noting that the half-integer "m" states vanish as required …
